A recent body of literature [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]} has analyzed the global and local convergence of ADMM approaches for non-convex instances of formulation (REF ).
It is well-understood by now (e.g., see [3]}) that for \(T > 2\) , convergence requires the existence of a block variable that is constrained only by the linear coupling equation, and whose objective function is globally Lipschitz differentiable.
Moreover, it must be coupled in such a way that it can “control” the iterates of the coupling constraints' dual variables (see Remark REF  later in the paper).
